The total cost (in dollars) for a company to manufacture and sell x items per week is C(x)=50x+400. If the revenue brought in by selling all x items is R(x)=80x-0.05x2, find the weekly profit. How much profit will be made by producing and selling 40 items each week? Hint: P(x)=R(x)−C(x).

$720

Step-by-step explanation:

Given the following functions

Cost function C(x)=50x+400

Revenue function R(x)=80x-0.05x^2

P(x)=R(x)−C(x).

Profit function P(x) = 80x-0.05x^2 - (50x+400)

P(x) = 80x-0.05x^2 - 50x - 400

Substitute x = 40

 P(40) = 80(40)-0.05(40)^2 - 50(40) - 400

P(40) = 3200-80-2000-400

P(40) =3200-2480

P(40) = 720

Hence the amount of profit made is $720